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Question 8: Consider the following feedback loop. Compensator Plant R(s) Σ K 100 Y(s) s+a s+50 Specify the gain and pole location of the compensator so that the overall closed-loop response to a unit step input has an overshoot of no more than 25% and a settling time of no more than 0.1 sec. may use the following relations and the plot below in your solutions. Rise time $t_r \approx \frac{1.8}{\omega_n}$, Peak time $t_p = \frac{\pi}{\omega_d}$, Settling time $t_s = \frac{4.6}{\sigma}$ 100 90 80 70 60 50 40 30 16% 20 5% 10 0 0.0 0.2 0.4 0.6 0.8 1.0

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2. The demand and the supply function of a good are given by: \[ Q_{D}=\frac{-P^{2}+5}{P+1}, \quad Q_{S}=P+1 \] a) Determine the equilibrium price and quantity. b) Determine the effect on the market equilibrium if the government decides to impose a subvention of \$3 on each good.

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Measuring cell sizes with an ocular micrometer Your microscope is equipped with a scale (called a reticule or ocular micrometer) that is built into one eyepiece. Ocular micrometers are uncalibrated measuring devices that can be used to measure any planar dimension in a microscope field, since the ocular can be turned in any direction and the object of interest can be repositioned with the stage manipulators. To measure the length of an object you simply note the number of ocular divisions spanned by the object, then multiply by the conversion factor for the magnification used. The conversion factor is different at each magnification. For very precise measurements, it is necessary to calibrate the ocular micrometer with a second micrometer (stage micrometer) that contains a ruler with known distances between lines on the scale. Looking through a lens at an object with an ocular micrometer in place would look something like this: 0 10 20 30 40 50 For the purpose of this lab, we are going to assume that the distance between the closest lines at 10 X is 10 µm. So, if a cell spanned the distance between the 10 and 20 on the ocular micrometer, that cell would be 10 lines X 10 µm per line or 100 µm in diameter. Under the 40 X objective the distance between lines becomes about 2.5 µm. If the 40 X objective is in place, what is the approximate diameter of the round "blob" that has been drawn in?

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Cost volume profit, analyst identifies, and measures cost using their fixed and variable components

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People begin to report the first signs of hunger when the stomach is ______ empty ? 10% ? 25% ? 40% ? 60%

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True of false? Once you mark a task as complete, it will no longer appear on your To-Do list. True O False

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-3x + 0y - 6z = 11 6x - 2y + 3z = 17 2x - y - 6z = -3 Use Cramer's rule to find the values of the variables x, y, and z (3 points each). Show the determinants involved clearly and expand the numerator determinants as follows to get any credit: For variable x, expand along the first column; for variable y, expand along the second column; for variable z, expand along the third column. You will receive 0 points if you expand these determinants any other way, even if your answer is correct.

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How market for a private good works vs optimum in quantity of public good works

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21 Since the onset of the Covid-19 pandemic and the invasion of Ukrain by Russia, inflation has become a serious problem in Canada and around the world. Assume that Statistics Canada reports that in 2021 the price level was 120 and the average nominal income was $30,000. In 2022, the price level was 125 and the average nominal level of income was $32,000. What happened to real income from 2021 to 2022? Multiple Choice It stayed constant. It fell by $400. It rose by $600. It rose by $400. It rose by $2,000.

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ABC Company currently just paid a dividend of $4.40 per share. ABC company's current payout ratio is 100%, so their earnings per share is $4.40 as well. Dividends are expected to remain constant indefinitely. Suppose the discount rate for ABC is 11 percent per year. What is the fundamental value of a share of ABC stock

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